Page 261 - Math_Genius_V1.0_C8_Flipbook

E:\Working\Focus_Learning\Math_Genius-8\Open_Files\13_Chapter_10\Chapter_10
\ 06-Jan-2025 Bharat Arora Proof-7 Reader’s Sign _______________________ Date __________

Learning by Doing

objective: To derive the formula for finding the area of a trapezium.
Materials Required: Graph paper or plain white sheet, geometry box and a pair
of scissors.

Procedure: Get into the pairs.
• Draw a trapezium PQRS on a graph paper as shown in figure and cut it out.

S R

P Q

Locate the mid-point K of side RQ and fold the paper along SK.

S R

K

P Q
• Cut the trapezium PQRS along SK into two pieces. Place the cut portion, that is, DSRK in
such a manner that the side KR is placed on KQ and PQ gets extended to L.

S

K

R L
P Q
observation:

Area of DSPL = 1 × Base × Height
2
Base of DSPL = PQ + QL = PQ + SR (Since QL = SR)
Height of DSPL = h = Height of the given trapezium
1
Therefore, area of DSPL = × h × (PQ + SR)
2
However, we notice that area of DSPL = Area of trapezium PQRS
1
So, area of trapezium PQRS = × h × (PQ + SR)
2
1
Thus, the area of trapezium = × height × sum of parallel sides
2

259 Mensuration